Calculate the power absorbed at t = 0−, t = 0+, and t = 200 ms by each of the elements in the circuit of Fig. 11.27 if vs is equal to (a) −10u(−t) V; (b) 20 + 5u(t) V.
■ FIGURE 11.27
(a)
Find the power absorbed at
Answer to Problem 3E
The power absorbed at
The power absorbed at
The power absorbed at
Explanation of Solution
Given data:
Refer to Figure 11.27 in the textbook for the given circuit.
The circuit parameters are given as follows:
Formula used:
Write the expression for power absorbed by the voltage source as follows:
Here,
Write the expression for power absorbed by the resistor in the given circuit as follows:
Here,
Write the expression for conservation power in the circuit as follows:
Here,
Calculation:
Find the source voltage at
Write the expression for current through each element in the given circuit as follows:
Here,
Write the expression for time constant in the given circuit as follows:
Substitute
From the given circuit, the initial value of the current is determined as follows:
From the given data, substitute
Substitute
Find the current
Modify the expression in Equation (1) for
Substitute
Modify the expression in Equation (2) for
Substitute
Rewrite the expression in Equation (3) as follows:
Here,
Rewrite the expression in Equation (6) for the power absorbed by the inductor as follows:
Modify the expression for
Substitute
Find the source voltage at
Substitute
Modify the expression in Equation (1) for
Substitute 0 V for
Modify the expression in Equation (2) for
Substitute
Modify the expression in Equation (7) for
Substitute 0 W for
Find the source voltage at
Substitute
Modify the expression in Equation (1) for
Substitute 0 V for
Modify the expression in Equation (2) for
Substitute
Modify the expression in Equation (7) for
Substitute 0 W for
Conclusion:
Thus, the power absorbed at
The power absorbed at
The power absorbed at
(b)
Find the power absorbed at
Answer to Problem 3E
The power absorbed at
The power absorbed at
The power absorbed at
Explanation of Solution
Given data:
The source voltage is given as follows:
Calculation:
Find the source voltage at
Write the expression for current through each element in the given circuit as follows:
From Part (a), substitute 0.25 s for
Find the current
Modify the expression in Equation (1) for
Substitute 20 V for
Modify the expression in Equation (2) for
Substitute 20 A for
Substitute
Find the source voltage at
Substitute
Modify the expression in Equation (1) for
Substitute 25 V for
Modify the expression in Equation (2) for
Substitute 20 A for
Modify the expression in Equation (7) for
Substitute
Find the source voltage at
Substitute
Modify the expression in Equation (1) for
Substitute 25 V for
Modify the expression in Equation (2) for
Substitute 22.7533 A for
Modify the expression in Equation (7) for
Substitute
Conclusion:
Thus, the power absorbed at
The power absorbed at
The power absorbed at
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Chapter 11 Solutions
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